Police said the 17-year-old Christopher Earl Glass abducted his baby in Palmdale about 11 a.m. and threatened to harm him.
Sheriff's deputies spotted the SUV at about 3:45 p.m. and gave pursuit for about three minutes. Glass crashed his SUV into a bus stop at the Palmdale Metrolink station on Clock Tower Plaza Drive.
Glass then exited the vehicle and fled on foot. Deputies say they saw him stabbing the baby as he ran into a house in the 500 block of East Avenue P-14.
Deputies chased Glass inside and one of them shot him.
The child, Christopher Earl Glass Jr., was transported to a hospital, where he was declared dead.
"The deputies were trying to do life-saving measures on the way to the hospital, said Nicole Nishida of the sheriff's department. "It was a very emotional time for one of the deputies who was there."
The sheriff's department said Glass also died.
Stunned family members stood at the Metrolink station trying to figure out why Glass would stab his own son to death.
"He loved that baby," said Denise Hudson, a relative. "There were times when I would visit my aunt, he would be holding the baby, feeding him, changing the diaper. He was a great dad. That's why it's a shock."
No deputies were injured.
The incident was under investigation.